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We show that the collectivity of the particle-hole wave function of low-lying octupole 3^{−} states in doubly magic nuclei is mainly due to the neutron-proton interaction. Both the enhanced reduced transition probability to the ground state, B(E3;3_{1}^{−}→0_{1}^{+}), and the coupling of the octupole excitation to a nucleon result from the coherent action of all the components of the collective state. The results obtained with a realistic shell-model interaction both for ^{208}Pb and for ^{209}Pb agree with the geometric collective model of Bohr and Mottelson, where octupole excitations are associated with phonons corresponding to collective shape oscillations of the surface of the nucleus.